A cartel is a group of firms that agree to act like a single monopoly — restrict output, lift the price, split the profit. The trouble is that the deal is never self-enforcing: on any given day each member earns more by quietly breaking it. Why cartels form, why they fall apart, and how repetition can hold one together is a favourite topic of the students who come to an economics tutor in Saudi Arabia.
1 · The cartel as a joint monopoly
A cartel exists to capture the profit competition destroys. Left to compete, firms drive the price toward marginal cost and the industry earns almost nothing. Acting as one, they pick the output where industry marginal revenue equals marginal cost — the monopoly quantity — hold the price above cost, and split the profit by quota. In a step: set MR = MC, solve for joint output, read the price off demand (the monopoly apparatus itself sits on our monopoly page). The restriction is the mechanism — to raise the price, you produce less than a competitive market would.
2 · Why the cartel is not self-enforcing
Give each member a quota and something uncomfortable appears. Hold the propped-up price fixed for a moment. Each firm sees a price far above its marginal cost, so one unit beyond quota adds nearly the whole price to revenue and only marginal cost to cost. Everyone has a private incentive to overproduce. When one does, output rises, the price falls, and the cheat grabs extra sales at the others’ expense — its one-period defection payoff beats its cartel share, as you compute below. In a single encounter, defecting is a dominant strategy for both, and the outcome is the prisoners’ dilemma (new to dominant strategies and Nash? start with our game-theory page). The non-cooperative resting point is the Cournot equilibrium; we derive those reaction functions on the Cournot page, so here you need only its payoff.
3 · Repetition, grim triggers and the folk theorem
What breaks the dilemma is that real rivals meet again and again, so today’s action can be punished tomorrow. The simplest punishment is the grim trigger: hold your quota as long as everyone has; the first period anyone cheats, revert to Cournot forever. Now weigh cooperating forever, which banks your cartel share every period, against cheating once — you seize the large defection payoff, then live on Cournot profit for good. Which wins turns on the discount factor δ, how much a firm values next period against this one (or the chance the relationship continues). Patient firms fear the forfeited future rents; impatient ones take the money and run. Cooperation survives exactly when δ ≥ (πdefect − πcartel)/(πdefect − πNash). The folk theorem generalises this: with patient enough players, essentially any outcome giving each at least their punishment payoff can be sustained as an equilibrium. Repetition makes cooperation possible — not inevitable, and not unique.
4 · What makes collusion easier or harder
Whether a real cartel holds depends on how fast cheating is spotted and how credibly it is punished. Collusion is easier when firms are few and similar: a common quota is obvious, and each share is large against the one-shot temptation. It is easier when cheating is visible quickly — posted prices, steady demand — so punishment lands before the cheat banks much. It is harder when demand is volatile, since a price fall might be a defection or just weak demand, and that detection lag blunts the threat. It is harder when firms differ in cost, because they disagree on the right price — and hardest when the punishment is not credible, since a threat no one would carry out deters no one.
5 · Competition policy and leniency
Because cartels transfer surplus away from buyers and waste the gains competition would deliver, they are illegal in most jurisdictions, and competition authorities work to detect and prosecute them. The sharpest tool is the leniency programme: the first member to confess and cooperate is offered immunity or a steep penalty cut. Read through the repeated game, leniency attacks the trigger strategy itself — it rewards the first defector, so each member fears the others will race to confess. That fear can unravel an agreement the market alone would have held.
Worked example — two ready-mix concrete plants
Two plants supply ready-mix concrete to a city’s building sites. Weekly inverse demand is P = 80 − Q, with Q = q₁ + q₂ the total output in thousand m³ and P the price in £ per m³. Each plant’s marginal cost is a constant c = 20, no fixed costs. (Quantities in thousand m³ per week, so profit is in £000 per week.)
Step 1 — Competitive benchmark. If rivalry drove the price to cost, P = 20, so 80 − Q = 20 and Q = 60. Price equals cost; profit is zero. This is what the cartel wants to escape.
Step 2 — The cartel as joint monopoly. As one firm, the plants maximise (P − c)Q = (80 − Q − 20)Q. Setting MR = 80 − 2Q = 20 gives Q = 30 and P = 50, for total profit (50 − 20) × 30 = 900. Cutting output from 60 to 30 is what lifts the price from 20 to 50.
Step 3 — Quota and prize. Split output and profit equally: each plant makes 15 and earns (50 − 20) × 15 = 450 a week — against nothing under competition. Call 450 the cartel share.
Step 4 — The temptation. Hold your partner at its 15 quota and choose your own output to maximise (80 − (q₁ + 15) − 20)q₁ = (45 − q₁)q₁. The condition 45 − 2q₁ = 0 gives q₁ = 22.5. Producing 22.5 instead of 15 lifts total output to 37.5, drops the price to 42.5, and earns (42.5 − 20) × 22.5 = 506.25 — against the 450 you keep by honouring the deal.
Step 5 — Collapse, and the fix. Both plants see 506.25 > 450, so in one period both defect. The non-cooperative outcome is Cournot: each produces 20, price 40, profit 400 — below the promised 450. So πdefect = 506.25 > πcartel = 450 > πNash = 400. Now let the plants meet weekly under a grim trigger. Cooperating forever is worth 450/(1 − δ); cheating once is worth 506.25 + δ × 400/(1 − δ). Cooperation holds when 450/(1 − δ) ≥ 506.25 + δ·400/(1 − δ), i.e. δ ≥ (506.25 − 450)/(506.25 − 400) = 56.25/106.25 = 9/17 ≈ 0.53.
Step 6 — Interpretation. The cartel is self-enforcing only if each plant weights the future heavily enough — δ of at least about 0.53. Below that, the quick 56.25 gain from cheating beats the discounted cartel rents it forfeits, and no deal holds. Above it, the threat of permanent Cournot punishment keeps both honest with no contract and no regulator — only patience and a credible threat. Note what the threshold ignores: for this symmetric linear market, 9/17 is the same whatever the demand intercept or cost level. Structure, not the numbers, sets the bar.
Could you compute the defection payoff, stack it against the cartel share, and derive the discount factor that keeps the deal alive? That chain — the temptation, the reward, the punishment — is exactly what repeated-game questions test. A one-on-one economics tutor builds the grim-trigger condition from the profit functions with you until the threshold falls out on its own. Book a trial session.
Practice
Q1. In the concrete market above, each plant values next week at δ = 0.5. Is the cartel sustainable under grim trigger?
Q2. A third identical plant joins, and the cartel splits monopoly output three ways. Find each firm’s cartel share, its defection payoff (the others holding quota), the Cournot punishment profit, and the new threshold δ*. Easier or harder?
Q3. In a different market, P = 130 − Q with c = 10 and two firms, find the grim-trigger threshold δ*.
Answers. Q1: cooperating is worth 450/(1 − 0.5) = 900; defecting, 506.25 + 0.5 × 400/0.5 = 906.25. Since 906.25 > 900, cheating pays — not sustainable, as δ = 0.5 sits just below 9/17 ≈ 0.529. Q2: output 30 split three ways is a quota of 10 and a share of 900/3 = 300; with rivals at 10 each, your best reply solves 40 − 2q = 0, so q = 20, price 40, defection payoff (40 − 20) × 20 = 400; three-firm Cournot gives 15 each at price 35, profit 225. So δ* = (400 − 300)/(400 − 225) = 100/175 = 4/7 ≈ 0.571 — above 9/17, so collusion is harder with more firms. Q3: monopoly output 60, share 1800; Cournot profit 1600 each; defection payoff 2025 (best reply 45 while the partner holds 30). δ* = (2025 − 1800)/(2025 − 1600) = 225/425 = 9/17 ≈ 0.529 — identical to the base case, because for a symmetric linear duopoly the threshold is independent of the demand and cost figures.
Key takeaways
- A cartel is a joint monopoly. It restricts output to where industry MR = MC, holds the price above cost, and splits the profit — capturing the rents competition would have destroyed.
- It is never self-enforcing in one shot. Each member’s defection payoff (506.25) beats its cartel share (450), so defecting dominates and the market settles at Cournot (400 each).
- Repetition is the fix. Under grim trigger, cooperation is an equilibrium when δ ≥ (πdefect − πcartel)/(πdefect − πNash) — here 9/17 ≈ 0.53. Patience and a credible punishment stand in for a contract.
- Structure sets the threshold. More firms raise the required δ; volatile demand, cost asymmetry and slow detection push the same way. The folk theorem makes cooperation possible, not guaranteed.
Why students in Saudi Arabia choose our economics tutoring
- Models derived, not memorised: sessions build the grim-trigger condition from the profit functions, so you can reproduce δ* under exam pressure instead of quoting a formula.
- The distinctions examiners test, drilled: one-shot versus repeated games, cartel share versus defection payoff, folk-theorem possibility versus inevitability — the lines that separate a first from a 2:1.
- Online, wherever you study: one-on-one sessions run for students in Riyadh, Dammam and Jeddah, matched to your university’s syllabus and past papers.
FAQ
Q: Why isn’t a cartel stable on its own?
A: Because every member can earn more by breaking the deal. With the price held above marginal cost, producing a little beyond your quota adds nearly the full price to revenue, so cheating pays in any single period. If all reason this way, the cartel collapses to the Cournot outcome.
Q: What is a grim-trigger strategy?
A: Cooperate — stick to your quota — for as long as everyone else has. The first time anyone cheats, switch to the Cournot outcome forever. It is the harshest credible punishment, and it makes cooperation an equilibrium when firms are patient enough.
Q: What does the discount factor δ mean?
A: How much a firm values profit next period relative to this one, between 0 and 1 — or the probability the relationship continues. A higher δ means the future matters more, so the threat of forfeited profit deters cheating.
Q: Does the folk theorem mean cartels always survive?
A: No. With patient enough players, cooperation can be sustained as an equilibrium — alongside many other outcomes. It establishes possibility, not inevitability; whether a real cartel holds turns on detection, symmetry and credible punishment.
Q: How do leniency programmes fight collusion?
A: They offer the first firm to confess immunity or a large penalty cut. That rewards defection and makes each member fear the others will report first, which can unravel an agreement the market alone would have sustained.
Book an economics tutor in Saudi Arabia or online
Repeated games reward students who can derive the sustainability condition, not just name it — the cartel share, the defection payoff, the Cournot punishment, and the discount factor that ties them together. One-on-one sessions build that fluency on your own past papers. Tell us your course and exam date, and we will match you with the right tutor this week.
